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Which set is closed under the given operation 1 integers under division 2 negative integers under subtraction 3 odd integers under multiplication?
1 No. 2 No. 3 Yes.
Are odd numbered sets closed under multiplication?
Yes
Are odd numbered sets closed under addition and multiplication?
No. 1 + 3 = 4, which is not odd. In fact, no pair of odds sums to an odd. So the set is not closed under addition.
Is the set of odd numbers is closed under multiplication but is not under addition?
Let + (addition) be a binary operation on the set of odd numbers S. The set S is closed under + if for all a, b ϵ S, we also have a + b ϵ S. Let 3, 5 ϵ the set of odd numbers 3 + 5 = 8 (8 is not an odd number) Since 3 + 5 = 8 is not an element of the set of the odd numbers, the set of the odd numbers is not closed under addition.
Why is an odd number times an odd number an odd number?
Suppose m and n are integers. Then 2m + 1 and 2n +1 are odd integers.(2m + 1)*(2n + 1) = 4mn + 2m + 2n + 1 = 2*(2mn + m + n) + 1 Since m and n are integers, the closure of the set of integers under multiplication and addition implies that 2mn + m + n is an integer - say k. Then the product is 2k + 1 where k is an integer. That is, the product is an odd number.
Why are odd integers closed under multiplication but not under addition?
The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.
Which set is closed under the given operation 1 integers under division 2 negative integers under subtraction 3 odd integers under multiplication?
1 No. 2 No. 3 Yes.
ARe odd integers not closed under addition?
That is correct, the set is not closed.
Are odd numbered sets closed under multiplication?
Yes
Under which operation is the set of odd integers closed?
addition
Are odd numbered sets closed under addition and multiplication?
No. 1 + 3 = 4, which is not odd. In fact, no pair of odds sums to an odd. So the set is not closed under addition.
Why the set of odd integers under addition is not a group?
Because the set is not closed under addition. If x and y are odd, then x + y is not odd.
Is the set of odd integers closed under division?
No. For example, 5 is an odd integer and 3 is an odd integer, yet 5/3 is neither an integer nor odd (as odd numbers are, by definition, integers).
Is the set of odd numbers closed under multiplication?
Yes.To say a set is closed under multiplication means that if you multiply any 2 numbers in the set, the answer will always be a member of the set. When you multiply 2 odd numbers, the answer is always an odd number, so the set is closed.It must be the same person asking these questions!Read more: Is_the_set_of_odd_integers_closed_under_subtraction
Is the set of odd numbers is closed under multiplication but is not under addition?
Let + (addition) be a binary operation on the set of odd numbers S. The set S is closed under + if for all a, b ϵ S, we also have a + b ϵ S. Let 3, 5 ϵ the set of odd numbers 3 + 5 = 8 (8 is not an odd number) Since 3 + 5 = 8 is not an element of the set of the odd numbers, the set of the odd numbers is not closed under addition.
Why is an odd number times an odd number an odd number?
Suppose m and n are integers. Then 2m + 1 and 2n +1 are odd integers.(2m + 1)*(2n + 1) = 4mn + 2m + 2n + 1 = 2*(2mn + m + n) + 1 Since m and n are integers, the closure of the set of integers under multiplication and addition implies that 2mn + m + n is an integer - say k. Then the product is 2k + 1 where k is an integer. That is, the product is an odd number.
Give two reason for the set of odd integers is not a group?
Assuming that the question is in the context of the operation "addition", The set of odd numbers is not closed under addition. That is to say, if x and y are members of the set (x and y are odd) then x+y not odd and so not a member of the set. There is no identity element in the group such that x+i = i+x = x for all x in the group. The identity element under addition of integers is zero which is not a member of the set of odd numbers.
